You are given a problem to show that vectors are "linearly dependent" or "linearly independent" and no one has ever told you what those words mean? How awful of them! I recommend you look up the words in your text book!

My point was that you asked "What does that mean?" in reference to a problem about independence! I could only interpret that as asking what "independence" meant.

Simplified I know it as:
Vectors in V are linearly dependant if there are scalars that do not equal zero.

Otherwise the vectors are linearly independant, if all the scalars have to equal zero.

That's way over simplified. There are always scalars that are not equal to zero! You mean "If a linear combination of the vectors (sum of scalars times the vectors) is equal to 0, with not all the scalars being 0, then the vectors are dependent" and the opposite for independence. It is important to mention that the scalars are in the linear combination and that the linear combination is equal to 0.